THE SENSE OF HEARING. 813 



concerned in the lever action. The bony lever being thus balanced, it is less 

 difficult to understand its known sensitiveness to impulses that are inconceivably 

 weak. The tense tympanic membrane, by reason of its funnel shape, resists 

 strong inward compression ; hence the stapes is prevented from being pressed 

 too far inward. The maximum amplitude of motion of the stapes in the 

 fenestra is very small, being only about y 1 ^ millimeter to -fa millimeter, while 

 that of the centre of the tympanic membrane is about ^ millimeter to ^ 

 millimeter. 



The functional movements of the auditory ossicles are not molecular but 

 are molar vibrations, the chain of bones moving in a body. The sole purpose 

 of this apparatus of the middle ear is to transmit exactly the variations of 

 pressure in the air of the external auditory meatus to the peri lymph which 

 bathes the foot of the stapes in other words, to convert air-waves into a 

 similar series of water-waves. In the words of Helmholtz, 1 " The mechanical 

 problem which the apparatus within the drum of the ear had to solve was to 

 transform a motion of great amplitude and little force, such as impinges on 

 the drum-skin, into a motion of small amplitude and great force, such as had 

 to be communicated to the fluid in the labyrinth." 



The adaptation of the apparatus of the middle ear to this end is worthy 

 of careful consideration. In the first place, it will be noticed that the area 

 of the fenestra ovalis which receives the impulses of the stapes is but a small 

 fraction of the surface of the tympanic membrane on which the air-waves- 

 impinge, the latter area being some fifteen to twenty times greater than the 

 former, so that the energy of air-motion is, in a fashion, concentrated. In the 

 second place, as previously observed, the lever mechanism of the auditory 

 ossicles is such that the movements of the end of the long process of the incus 

 have two-thirds the amplitude of those of the tip of the manubrium, but 

 about one and one-half times their force. It should also be noticed that the 

 membrane fastening the foot of the stapes in the fenestra is somewhat less 

 tense on the upper side, so that the top of the oval foot-piece has a freer 

 motion than the bottom, and the head of the stirrup rises slightly with inward 

 motions. In the third place, it has been demonstrated by Helmholtz 2 that the 

 shape of the tympanic membrane peculiarly adapts it for transforming weak 

 movements of wide amplitude into strong ones of small compass. For this 

 membrane is not a simple funnel depressed inwardly, but the radii are slightly 

 curved with the convexity outward, a shape chiefly due to the tension of the 

 elastic circular fibres of the membrane on its inner face, these being most 

 numerous toward the circumference. Air-waves beating upon this convexity 

 flatten the curve somewhat, and their whole energy must be concentrated, with 

 increased intensity but loss of motion, at the central point of the membrane. 

 This effect may be illustrated by holding a slightly-curved brass wire, several 

 inches in length, with its plane perpendicular to the surface of a table and 

 supported on its ends. When one end of the wire is held immovable, up-and- 

 down motions of the arch are transferred to the free end with diminished 

 1 Op. cit, p. 134. 2 Op. tit. 



